II. MUSE spectroscopy of blue horizontal branch stars in the core of ω Centauri and NGC6752

Aims. We want to study the population of blue horizontal branch (HB) stars in the centres of globular clusters (GC) for the first time by exploiting the unique combination of MUSE spectroscopy and HST photometry. In this work, we characterize their properties in the GCs omega Cen and NGC6752. Methods. We use dedicated model atmospheres and grids of synthetic spectra computed using a hybrid LTE/NLTE modeling approach to fit the MUSE spectra of HB stars hotter than 8000 K in both clusters. The spectral fits provide estimates of the effective temperature (T-eff), surface gravity (log g), and helium abundance of the stars. The model grids are further used to fit the HST magnitudes of the stars, that is, their spectral energy distributions (SEDs). From the SED fits, we derive the average reddening, radius, luminosity, and mass of the stars in our sample. Results. The atmospheric and stellar properties that we derive for the stars in our sample are in good agreement with theoretical expectations. In particular, the stars cooler than similar to 15 000 K closely follow the theoretical predictions on radius, log g, and luminosity for helium-normal (Y = 0.25) models. In. Cen, we show that the majority of these cooler HB stars cannot originate from a helium-enriched population with Y > 0.35. The properties of the hotter stars (radii and luminosities) are still in reasonable agreement with theoretical expectations, but the individual measurements show a large scatter. For these hot stars, we find a mismatch between the effective temperatures indicated from the MUSE spectral fits and the photometric fits, with the latter returning Teff lower by similar to 3000 K. We use three different diagnostics, namely the position of the G-jump and changes in metallicity and helium abundances, to place the onset of diffusion in the stellar atmospheres at T-eff between 11 000 and 11 500 K. Our sample includes two stars known as photometric variables; we confirm one to be a bona fide extreme HB object but the other is a blue straggler star. Finally, unlike what has been reported in the literature, we do not find significant differences between the properties (e.g., log g, radius, and luminosity) of the stars in the two clusters. Conclusions. We show that our analysis method - combining MUSE spectra and HST photometry of HB stars in GCs - is a powerful tool for characterising their stellar properties. With the availability of MUSE and HST observations of additional GCs, we have a unique opportunity to combine homogeneous spectroscopic and photometric data to study and compare the properties of blue HB stars in different GCs.